Multifractal analysis of the spectral measure of the Thue–Morse sequence: a periodic orbit approach

The Fourier spectral density of the Thue–Morse sequence is reinterpreted as the invariant measure of a stochastic dynamical system. Based on this fact, its generalized (Rényi) dimension and f(α) statistics are calculated with high precision by cycle expansions of spectral determinant and dynamical zeta function. αq at integer values of q are also computed in an operator scheme and the asymptotic result in the large-q limit is derived.